tone zone or JB should sound great in this guitar.
the fact that you're saying the jb doesn't sound good and the invader wasn't "invader ish" raises suspicion to me that you may have a wiring issue or a burned out pot.. those rampages sound really round and full with a JB in them. the invader is everything but thin and weak.
just an insight here....i had this issue in two of my les pauls. the stock wiring that connects two of the pots grounds together then to jack/ same wire inner is output from volume to jack, was somehow interfering with the signal chain.....it was that stock braided outer ground shield with the innner signal wire....it was fucked up for some reason. i checked continuity, and it was fine. wasnt shorting out at all. i tried it in another guitar, and it was the same shitty sound. i changed it out, and i was back to normal. the sound i experienced with the wiring problem was exactly what you described...like a humbucker that was only running one bobbin, very thin, lifeless and lacking. this was about 10 years ago. recently, i was swapping pickups, and the same thing happened, and i immediately pulled that wire and replaced it with some belden wire, and all was well.
point is, check your wiring with the JB still in there bro.